Pythagorean Theorem

Front

What is the Pythagorean Theorem?

Back

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). Formula: a² + b² = c².

Front

In a right triangle, which side is the hypotenuse?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.

Front

If one side of a right triangle is 6 and the other side is 8, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 6² + 8² = 36 + 64 = 100, so c = √100 = 10.

Front

What is the square root of 64?

Back

The square root of 64 is 8.

Front

If the hypotenuse of a right triangle is 13 and one side is 5, what is the length of the other side?

Back

Using the Pythagorean Theorem: 13² = 5² + b², so 169 = 25 + b², thus b² = 144, and b = √144 = 12.

Front

What does it mean to square a number?

Back

To square a number means to multiply the number by itself.

Front

What is the opposite operation of squaring a number?

Back

The opposite operation of squaring a number is taking the square root.

Front

If a right triangle has sides of length 9 and 12, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 9² + 12² = 81 + 144 = 225, so c = √225 = 15.

Front

What is the formula to find the area of a right triangle?

Back

The area of a right triangle is given by the formula: Area = (1/2) × base × height.

Front

In a right triangle, if one angle is 90 degrees, what are the other two angles?

Back

The other two angles must add up to 90 degrees, as the sum of angles in a triangle is always 180 degrees.